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Direct and skew sum operations are invaluable techniques for
linking permutations while retaining their original structure in the resulting concatenation. In this work we apply the direct and skew sum operations on the elements of the Γ1−non deranged permutation group (G
Γ1
p
),
and present relations and schemes on the structures and fixed points of
the permutations obtained from these operations. Furthermore, if π is the
direct sum of these Γ1− non deranged permutations, then the collection
of permutations in the form of π is an abelian group under composition,
denoted as G
m⊕
p
. We present an expression relating the direct and skew
sum operations, and we establish an isomorphism between G
Γ1
p × GΓ1
p
and
G
m⊕
p
.
Kazeem Olalekan Aremu, Stephen Buoro, Abor Isa Garba, Abdulkarim Hassan Ibrahim. (2018) On the Direct and Skew Sums of Γ1−Non Deranged Permutations, Punjab University Journal of Mathematics, Volume 50, Issue 3.
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